Nice find. That looks very similar. It looks like there were 3 different thermostats used in those things. It also had an overtemp thermostat, which I think that is what your picture is. I guess your main thermostat is missing.
I don't know what that is. If I was guessing, it would have to be a thermostat of some kind since it has little vent holes around it. It probably either has a bimetal disc or a bimetal spring like the old analog home thermostats. It probably has a bigger temperature swing than what you want anyways.
This is the heating element in red.
The power for the heating element is the white and blue lines. One of those wires should go back to some kind of thermostat. It may not be a wafer but could be smaller made with a bimetal disc in it like a water heater thermostat.
One of the two things...